A commuter attempts to catch the 8:00 am train every morning although his arrival time at the station is a random variable that is uniformly dis- tributed between 7:55 am and 8:05 am. The train's departure time from the station is also a random variable that is uniformly distributed between 8:00 am and 8:10 am. a) Find the probability density function of the time interval between the commuter's arrival at station and the train's departure time. b) Find the probability that the commuter will catch the train. c) If the commuter gets delayed 3 minutes by a traffic jam, find the probability that the train will still be at the station.
A commuter attempts to catch the 8:00 am train every morning although his arrival time at the station is a random variable that is uniformly dis- tributed between 7:55 am and 8:05 am. The train's departure time from the station is also a random variable that is uniformly distributed between 8:00 am and 8:10 am. a) Find the probability density function of the time interval between the commuter's arrival at station and the train's departure time. b) Find the probability that the commuter will catch the train. c) If the commuter gets delayed 3 minutes by a traffic jam, find the probability that the train will still be at the station.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:A commuter attempts to catch the 8:00 am train every morning although
his arrival time at the station is a random variable that is uniformly dis-
tributed between 7:55 am and 8:05 am. The train's departure time from
the station is also a random variable that is uniformly distributed between
8:00 am and 8:10 am.
a) Find the probability density function of the time interval between the
commuter's arrival at station and the train's departure time.
b) Find the probability that the commuter will catch the train.
c) If the commuter gets delayed 3 minutes by a traffic jam, find the
probability that the train will still be at the station.
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